Questions: The Gazelles are a professional soccer team based in a large city. At the team's home matches, children's admission is half-off. Among the 730 attendees at the last home match, 330 were children. At that match, the facilities manager took a sample of 47 attendees. He found that 27 of these attendees were children. For the facilities manager's sample, find and write with proper notation the sample proportion and population proportion of attendees who were children. Write the proportions as decimals (not percentages) rounded to two decimal places. (a) Sample proportion: (Choose one) = (b) Population proportion: (Choose one) =

The Gazelles are a professional soccer team based in a large city. At the team's home matches, children's admission is half-off. Among the 730 attendees at the last home match, 330 were children. At that match, the facilities manager took a sample of 47 attendees. He found that 27 of these attendees were children.

For the facilities manager's sample, find and write with proper notation the sample proportion and population proportion of attendees who were children. Write the proportions as decimals (not percentages) rounded to two decimal places.
(a) Sample proportion: (Choose one) =
(b) Population proportion: (Choose one) =

Transcript text: The Gazelles are a professional soccer team based in a large city. At the team's home matches, children's admission is half-off. Among the 730 attendees at the last home match, 330 were children. At that match, the facilities manager took a sample of 47 attendees. He found that 27 of these attendees were children. For the facilities manager's sample, find and write with proper notation the sample proportion and population proportion of attendees who were children. Write the proportions as decimals (not percentages) rounded to two decimal places. (a) Sample proportion: (Choose one) $\boldsymbol{\nabla}=$ $\square$ (b) Population proportion: (Choose one) $\boldsymbol{\nabla}=$ $\square$

Solution

Solution Steps

To find the sample proportion, divide the number of children in the sample by the total number of attendees in the sample. For the population proportion, divide the total number of children by the total number of attendees at the match. Both proportions should be rounded to two decimal places.

Step 1: Calculate the Sample Proportion

To find the sample proportion of attendees who were children, use the formula:

\[ \text{Sample Proportion} = \frac{\text{Number of Children in Sample}}{\text{Total Sample Size}} \]

Substituting the given values:

\[ \text{Sample Proportion} = \frac{27}{47} \approx 0.5745 \]

Rounding to two decimal places, the sample proportion is:

\[ \boxed{0.57} \]

Step 2: Calculate the Population Proportion

To find the population proportion of attendees who were children, use the formula:

\[ \text{Population Proportion} = \frac{\text{Total Number of Children}}{\text{Total Number of Attendees}} \]

Substituting the given values:

\[ \text{Population Proportion} = \frac{330}{730} \approx 0.4521 \]